The twenty-seven lines upon the cubic surface ... by Archibald Henderson.

THE LINES UPON THE CUBIC SURFACE 7

71

x y z IV Co-ordinates, for edge= 100

0 is line CD
5 meets BD
BC
1 passes through D
meets ABC
2 passes through D
meets A BC
3 passes through D
meets ABC
4 passes through D
meets ABC
1' passes through C
meets ABD
2' passes through C
meets ABD
3'passes through C
meets A BD
4' passes through C
meets A BD
12.3'4' meets BCD
ABC
13.2'4',,BCD
ABC
14. 2'3',,BCD
ABC
23.1I'4', BCD
ABD
24. 1'3',,BCD
ABD
34. 1'2',,BCD

5
5
5
3
3
1
3
8085
15
5
15
9

3
1
10
15
20
3
6
3
12
630
13860
5
20
3
6
3
18
15
12

4
2
8
18
32

10

756
10164
8
14
6
4
6
36

1
4
3
16
1 470
10
5
3
1 0
20
7

y=23, w=77
y=20, z=80
x =36-1, y =36l1, z =14-4
x~= 18-8, y=37-7, z=30-1
x=11-4, y=3412, z==41
v='7-6, y=30O4, z=48-6
x=37-1,y1=37-1, wv=12A4
x=20, y=4O, w)26-6
x=1214,~y=37l1, w=37-1
x=8-4, y=35 w=44-7
y=19-1, z=22-9, w=44'6.v=21-8, Y=37-4, z=27-4
y=18S8, z=30-1, w=37-7
x=26-5, y=35.4, z==24-7
y=18-6, z=37-1, wv=30-9
x=28-9, y=34-6, z=23-1
y=18-6, z=37-1, w=30-9
x=30-2,~y=36-3 w==20-1
y=l8-3, z=43-9, w=24-4
x =27 8 y = 371, w =21U6
y/=18l1, z =50-5, w =18-1
xv=23, g=39-5,w=24-1

5

14 5
10164

15 ABD 9702 16632